Latitude E6500 won't boot; flashing Numlock

Starting last night, my Latitude E6500 will not boot. On pressing the button, the CPU light sometimes blinks for just an instant, but never for long. After that, I hear the fan running for a few seconds while the power light remains on, but nothing is on the screen whatsoever. Then, the fan stops, the power light goes off, and I am left with solid Caps and Scroll lock lights and a flashing Numlock light. This lasts for about 30 seconds or so, and then also goes off, leaving the computer completely off. I was able to successfully charge the computer (it had a half charge when this started), and it now has a full charge. What could be wrong? Thank you.

On pressing the button, the CPU light sometimes blinks for just an instant, but never for long. After that, I hear the fan running for a few seconds while the power light remains on, but nothing is on the screen whatsoever. Then, the fan stops, the power light goes off.

I'm very sorry for your latitute. For mine the problem was the motherboard. I have the laptop already here in office, waiting for dismiss, because I was out of warranty, and Dell asked me too much to repair it. So I bought another laptop.

I have the same problem -- but only if I turn off and try to turn back on. I can keep tring and it might work, or I just let it sit (and presumably cool down) for several hours and it works fine. I think it is a problem with temperature sensing maybe? This has been happening for a couple years.Since I only use at home, and rarely need to power down and back up, it's not too big a problem for me, but sure would like to solve it!